Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The difference, union, and intersection of two classes
The union of two classes
elun2
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elunant
Metamath Proof Explorer
Ascii
Structured
Theorem
elun2
Description:
Membership law for union of classes.
(Contributed by
NM
, 30-Aug-1993)
Ref
Expression
Assertion
elun2
⊢
(
𝐴
∈
𝐵
→
𝐴
∈ (
𝐶
∪
𝐵
) )
Proof
Step
Hyp
Ref
Expression
1
ssun2
⊢
𝐵
⊆ (
𝐶
∪
𝐵
)
2
1
sseli
⊢
(
𝐴
∈
𝐵
→
𝐴
∈ (
𝐶
∪
𝐵
) )